The science center has 300 people in attendance on Tuesday. This is 150 percent of the attendance on Monday. Natasha is trying to figure out how many people were in attendance on Monday. Her work is shown below.

Question

StartFraction part Over whole EndFraction = StartFraction 150 Over 100 EndFraction

StartFraction 150 times 2 Over 100 times 3 EndFraction = StartFraction 300 Over question mark EndFraction

Since 150 times 2 = 300, then 100 times 3 or 300 people were in attendance on Monday.

What mistake did Natasha make?
Natasha should have multiplied 100 by 2.
Natasha should have divided 150 by 3.
Natasha should have added 150 and 300.
Natasha should have multiplied 300 and 150 percent.

Answer 1

To assess Natasha's work, let's clarify the problem and the correct way to solve it.

The problem states that the attendance on Tuesday (300 people) is 150% of the attendance on Monday. To find out how many were in attendance on Monday, we can set up the equation based on the percentage:

Let $x$ be the attendance on Monday. The equation reflecting that 300 is 150% of $x$ can be expressed as:

$$300=1.5x$$

To solve for $x$, you can divide both sides by 1.5:

$$x=\frac{300}{1.5}$$ $$x=200$$

So, the attendance on Monday was 200 people.

Now, let's evaluate Natasha's work:

1. She started with the proportion that $300$ is $150$ of some unknown attendance.
2. She transformed $150$ into a fraction, which is fine: $\frac{150}{100}$.
3. However, when she set up the proportion, she incorrectly stated that $\frac{150\times 2}{100\times 3}=\frac{300}{?}$.

Here, Natasha made a mistake because:

• She multiplied $100$ by $3$ (which is not relevant in this context) and incorrectly concluded the attendance for Monday.

Thus, the best choice among the options given is:

Natasha should have multiplied 100 by 2.

This is because if she were to find the attendance on Monday, she would need to understand that $150$ of something (the attendance of Monday) equals the attendance on Tuesday (300), leading to $x=300/1.5$, which corresponds to calculating it differently by multiplying the entire attendance by $\frac{100}{150}$.